What really matters is the motivation and how exactly the event took place. The police would do a thorough investigation into their backgrounds and histories, trying to find some reason or motive behind the killings. If it doesn't work out, however, then it would just be listed as an unsolved (cold) case.
I'm working on my criminal justice degree, so I have had some level of experience and knowledge on topics like these. That doesn't mean I'm necessarily RIGHT, but I am fairly certain that's what would happen. In the UK, however, they might do things a little differently.